vertical tangent line

[bodels]

So, I had a similar question to this on a test and couldn't figure it out. Any help would be appreciated.

Determine the point(s) where the curve x+y^3-y=1 has a vertical tangent line.

 

[galactus]

I assume you know how to differentiate, implicitly, the function at hand.

\(\displaystyle \frac{dy}{dx}=\frac{-1}{3y^{2}-1}\)

Now, if the tangent line is vertical, the slope is 'infinite'.

So, we set the denominator of dy/dx equal to 0 and solve for y.

Sub this y value back into the function and solve for x to find the corresponding x value(s).

 

[bodels]

Thank you!! I appreciate your time! I finally figured it out by looking at some other examples as well.